Great question, Barath! Paradoxes always operate by playing on your expectations, providing a situation or scenario that runs counter to what you'd naturally, logically believe would be the case. So viewed from that perspective, the similarities and differences idea is essentially this: sometimes you're given information where you would reasonably expect two things to be paired up or to coexist, and other times you would expect the opposite, two things that don't seem like they should go together...and the paradox then becomes either "these things I thought would be a pair are in fact separate or happening independently," or "these things I didn't expect to exist in tandem are happening together."
The first case is a surprising difference (or you could call/think of it as a separation or absence), while the second is an unexpected similarity (in other words, a partnership or simultaneity, etc). To explain a difference you wouldn't have predicted, you need some active agent of differentiation...something to split the two things you thought would go together. To explain a counterintuitive similarity you need an active cause for coexistence...something to link the things you expected to be separate. The explanation is often a change to one of the two pieces, however in the differences scenario it's a change that drives a wedge between the two, and in the similarities it's a change that draws the two closer together.
And most paradoxes will fit one of those forms! Simply ask yourself what's odd about the situation presented, and the oddity of it will likely be an unexpected pairing or an unexpected split. And once you have that you know what the right answer needs to do: combine the elements so that their partnership makes more sense, or divide the things so that their existing independently becomes more understandable.
I'll give you an example off the top of my head: suppose I tell you that gasoline prices are at an all-time high, and yet the average motorist actually spends less money on gas now than they did ten years ago. Weird, right? You'd expect with prices at historical highs the amount spent would have increased too...but no. So those two facts present an unexpected coexistence--an item costs more than ever but less is being spent on it--and we then need an explanation that helps reconcile the pair in tandem, likely some notion about driver behavior that could offset the high price of fuel. Maybe people drive less now, or take more public transportation, or own electric vehicles in high numbers. Any of those new facts would more comfortably allow the situation in question to occur and help explain how it came to be.
So to sum up, first, don't stress the details of similarities vs differences, but rather make it a priority every time to simply pinpoint what about the situation is paradoxical in the first place. Ask yourself "why is this different compared to what I would've expected?" And once you have the discrepancy in hand you'll be well on your way to spotting the cause of it, whether that cause is a joiner or a divider
Jon Denning
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